{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T10:10:21Z","timestamp":1771495821187,"version":"3.50.1"},"reference-count":42,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012165","name":"Key Technologies Research and Development Program","doi-asserted-by":"publisher","award":["2022YFB3306101"],"award-info":[{"award-number":["2022YFB3306101"]}],"id":[{"id":"10.13039\/501100012165","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52475279"],"award-info":[{"award-number":["52475279"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1016\/j.engappai.2026.114122","type":"journal-article","created":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T08:11:14Z","timestamp":1770624674000},"page":"114122","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Versatile electromagnetic vortex beamforming for phased array using hybrid neural network-based modeling and optimization"],"prefix":"10.1016","volume":"169","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3988-2744","authenticated-orcid":false,"given":"Le","family":"Kang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengyao","family":"Dai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinhuai","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.114122_bib1","doi-asserted-by":"crossref","first-page":"5340","DOI":"10.1109\/TMTT.2022.3216864","article-title":"High-order deep recurrent neural network with hybrid layers for modeling dynamic behavior of nonlinear high-frequency circuits","volume":"70","author":"Charoosaei","year":"2022","journal-title":"IEEE Trans. Microw. Theor. Tech."},{"key":"10.1016\/j.engappai.2026.114122_bib2","doi-asserted-by":"crossref","first-page":"6932","DOI":"10.1109\/TWC.2020.3007026","article-title":"Multi-mode OAM radio waves: generation, angle of arrival estimation and reception with UCAs","volume":"19","author":"Chen","year":"2020","journal-title":"IEEE Trans. Wireless Commun."},{"key":"10.1016\/j.engappai.2026.114122_bib3","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TAP.2023.3330344","article-title":"Synthesis of a thinned prephased electronically steered phased array using excitation control of both the small amplitude dynamic range ratio and low-resolution phase","volume":"72","author":"Cheng","year":"2024","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib4","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1049\/el.2019.0190","article-title":"Analysis of a uniform rectangular array for generation of arbitrary orbital angular momentum (OAM) modes","volume":"55","author":"Cho","year":"2019","journal-title":"Electron. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib5","series-title":"Proc. IEEE 97th Vehicular Technology Conf. (VTC2023-Spring)","first-page":"1","article-title":"Number of FLOPs of training DNNs for learning precoding","author":"Cong","year":"2023"},{"key":"10.1016\/j.engappai.2026.114122_bib6","doi-asserted-by":"crossref","first-page":"4355","DOI":"10.1109\/TAP.2022.3140214","article-title":"Synthesis of mask-constrained pattern-reconfigurable nonuniformly spaced linear arrays using artificial neural networks","volume":"70","author":"Cui","year":"2022","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib7","doi-asserted-by":"crossref","DOI":"10.1016\/j.phycom.2025.102835","article-title":"A jamming method for OAM communication system using genetic algorithm","volume":"73","author":"Dang","year":"2025","journal-title":"Phys. Commun"},{"key":"10.1016\/j.engappai.2026.114122_bib8","doi-asserted-by":"crossref","first-page":"144015","DOI":"10.1109\/ACCESS.2020.3013880","article-title":"An ANN-based synthesis method for nonuniform linear arrays including mutual coupling effects","volume":"8","author":"Gong","year":"2020","journal-title":"IEEE Access"},{"key":"10.1016\/j.engappai.2026.114122_bib9","article-title":"Vehicular intelligence in 6G: networking, communications, and computing","volume":"33","author":"Guo","year":"2022","journal-title":"Veh. Commun"},{"key":"10.1016\/j.engappai.2026.114122_bib10","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/LAWP.2023.3316136","article-title":"A millimeter-wave vortex phase imaging method developed for lateral resolution enhancement","volume":"23","author":"Hu","year":"2024","journal-title":"IEEE Antenn. Wireless Propag. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib11","article-title":"Scaling laws for neural language models","author":"Kaplan","year":"2020","journal-title":"arXiv preprint arXiv:2001.08361"},{"key":"10.1016\/j.engappai.2026.114122_bib12","doi-asserted-by":"crossref","first-page":"5637","DOI":"10.1109\/TAP.2025.3570199","article-title":"On the application of radon transformation for the synthesis of thinned planar antenna arrays","volume":"73","author":"Kedar","year":"2025","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib13","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1109\/JSSC.2022.3141366","article-title":"A 0.31-THz orbital-angular-momentum (OAM) wave transceiver in CMOS with bits-to-OAM mode mapping","volume":"57","author":"Khan","year":"2022","journal-title":"IEEE J. Solid State Circ."},{"key":"10.1016\/j.engappai.2026.114122_bib14","doi-asserted-by":"crossref","first-page":"5420","DOI":"10.1109\/TAP.2025.3555882","article-title":"Machine learning assisted synthesis of large non-uniform antenna arrays including mutual coupling with an equivalent small array model","volume":"73","author":"Li","year":"2025","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib15","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1109\/TMTT.2023.3300193","article-title":"A broadband dual-polarized reflective metasurface for THz OAM communication","volume":"72","author":"Li","year":"2024","journal-title":"IEEE Trans. Microw. Theor. Tech."},{"key":"10.1016\/j.engappai.2026.114122_bib16","doi-asserted-by":"crossref","DOI":"10.1016\/j.aeue.2023.155068","article-title":"Hybrid ANN-GA optimization method for minimizing the coupling in MIMO antennas","volume":"175","author":"Liu","year":"2024","journal-title":"AE\u00dc, Int. J. Electron. Commun."},{"key":"10.1016\/j.engappai.2026.114122_bib17","series-title":"2022 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"4932","article-title":"Nonuniform-to-uniform quantization: towards accurate quantization via generalized straight-through estimation","author":"Liu","year":"2022"},{"key":"10.1016\/j.engappai.2026.114122_bib18","article-title":"Pruning convolutional neural networks for resource efficient inference","author":"Molchanov","year":"2017","journal-title":"arXiv preprint arXiv:1611.06440"},{"key":"10.1016\/j.engappai.2026.114122_bib19","series-title":"2024 IEEE International Symposium on Phased Array Systems and Technology (ARRAY)","first-page":"1","article-title":"Vortex beam sidelobe suppression via bayliss synthesis from a rectangular phased array","author":"Nemitz","year":"2024"},{"key":"10.1016\/j.engappai.2026.114122_bib20","doi-asserted-by":"crossref","first-page":"89465","DOI":"10.1109\/ACCESS.2022.3197653","article-title":"A review of orbital angular momentum vortex waves for the next generation wireless communications","volume":"10","author":"Noor","year":"2022","journal-title":"IEEE Access"},{"key":"10.1016\/j.engappai.2026.114122_bib21","doi-asserted-by":"crossref","first-page":"3987","DOI":"10.1109\/TAP.2024.3375960","article-title":"An efficient optimization method for HCC antennas using quantum genes based on sparse artificial neural networks","volume":"72","author":"Peng","year":"2024","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib22","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1109\/TMTT.2023.3313869","article-title":"Data-driven optimization strategies for tunable RF systems","volume":"72","author":"Pirrone","year":"2024","journal-title":"IEEE Trans. Microw. Theor. Tech."},{"key":"10.1016\/j.engappai.2026.114122_bib23","doi-asserted-by":"crossref","first-page":"4751","DOI":"10.1109\/TMTT.2022.3200040","article-title":"Homotopy optimization and ANN modeling of millimeter-wave SIW cruciform coupler","volume":"70","author":"Roy","year":"2022","journal-title":"IEEE Trans. Microw. Theor. Tech."},{"key":"10.1016\/j.engappai.2026.114122_bib24","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/JETCAS.2020.2973391","article-title":"Programmable high-order OAM-carrying beams for direct-modulation wireless communications","volume":"10","author":"Shuang","year":"2020","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"10.1016\/j.engappai.2026.114122_bib25","doi-asserted-by":"crossref","first-page":"3242","DOI":"10.1109\/LAWP.2024.3433013","article-title":"ANN-assisted iterative algorithms for pattern synthesis of conformal arrays","volume":"23","author":"Sun","year":"2024","journal-title":"IEEE Antenn. Wireless Propag. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib26","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/LAWP.2024.3495494","article-title":"A novel method for controlling the divergence angle of multimode vortex beams","volume":"24","author":"Tao","year":"2025","journal-title":"IEEE Antenn. Wireless Propag. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib27","doi-asserted-by":"crossref","first-page":"779","DOI":"10.23919\/JSEE.2021.000067","article-title":"Broadband beam steering for misaligned multi-mode OAM communication systems","volume":"32","author":"Tian","year":"2021","journal-title":"J. Syst. Eng. Electron."},{"key":"10.1016\/j.engappai.2026.114122_bib28","series-title":"2023 Cross Strait Radio Science and Wireless Technology Conference (CSRSWTC)","first-page":"1","article-title":"Aperture field discretization method for array antenna using genetic algorithm","author":"Wang","year":"2023"},{"key":"10.1016\/j.engappai.2026.114122_bib29","doi-asserted-by":"crossref","DOI":"10.1016\/j.measurement.2021.110600","article-title":"OAM radar based fast super-resolution imaging","volume":"189","author":"Wang","year":"2022","journal-title":"Measurement"},{"key":"10.1016\/j.engappai.2026.114122_bib30","doi-asserted-by":"crossref","first-page":"3735","DOI":"10.1109\/TWC.2023.3310912","article-title":"Enabling more users to benefit from near-field communications: from linear to circular array","volume":"23","author":"Wu","year":"2024","journal-title":"IEEE Trans. Wireless Commun."},{"key":"10.1016\/j.engappai.2026.114122_bib31","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1109\/LCOMM.2020.3009759","article-title":"Direct generation of OAM mode-group and its application in LoS-MIMO system","volume":"24","author":"Xiong","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib32","doi-asserted-by":"crossref","first-page":"7234","DOI":"10.1109\/TAP.2022.3164238","article-title":"Model construction, theoretical analysis, and miniaturized implementation of high-order deflected multivortex beams with uniform elliptical array","volume":"70","author":"Xue","year":"2022","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib33","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TAP.2021.3098604","article-title":"Arbitrary vortex beam synthesis with donut-shaped metasurface","volume":"70","author":"Yang","year":"2022","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib34","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.1109\/TMTT.2024.3484164","article-title":"A fast and high-resolution imaging method for electromagnetic vortex radar using uniform concentric circular arrays","volume":"73","author":"Yang","year":"2025","journal-title":"IEEE Trans. Microw. Theor. Tech."},{"key":"10.1016\/j.engappai.2026.114122_bib35","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1109\/TAP.2023.3335808","article-title":"Circularly polarized antenna array synthesis based on machine-learning-assisted surrogate modeling","volume":"72","author":"Yang","year":"2024","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib36","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1109\/TAP.2022.3225587","article-title":"Synthesis for OAM vortex electromagnetic waves based on fourier\u2013bessel expansion","volume":"71","author":"Yu","year":"2023","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib37","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1109\/LWC.2022.3151885","article-title":"UCA based OAM beam steering with high mode isolation","volume":"11","author":"Yu","year":"2022","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib39","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1109\/LAWP.2020.2972969","article-title":"Water spiral dielectric resonator antenna for generating multimode OAM","volume":"19","author":"Yu","year":"2020","journal-title":"IEEE Antenn. Wireless Propag. Lett."},{"key":"10.1016\/j.engappai.2026.114122_bib40","doi-asserted-by":"crossref","DOI":"10.1016\/j.physleta.2025.130428","article-title":"Stable divergence angle control of OAM vortex beams with different modes","volume":"541","author":"Zhao","year":"2025","journal-title":"Phys. Lett. A."},{"key":"10.1016\/j.engappai.2026.114122_bib41","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6463\/acebfe","article-title":"Metasurface modulator of frequency diverse multi-mode OAM beams with equal divergence angle for coincidence imaging","volume":"56","author":"Zhou","year":"2023","journal-title":"J. Phys. Appl. Phys."},{"key":"10.1016\/j.engappai.2026.114122_bib42","doi-asserted-by":"crossref","first-page":"6318","DOI":"10.1109\/TAP.2023.3280748","article-title":"Time-efficient multiplex orbital angular momentum beam synthesis with arbitrary-shaped array using multipole moment expansion","volume":"71","author":"Zhu","year":"2023","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"10.1016\/j.engappai.2026.114122_bib43","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2024.109381","article-title":"A survey of machine learning and evolutionary computation for antenna modeling and optimization: methods and challenges","volume":"138","author":"Zou","year":"2024","journal-title":"Eng. Appl. Artif. Intell."}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626004033?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626004033?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T08:50:57Z","timestamp":1771491057000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626004033"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":42,"alternative-id":["S0952197626004033"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.114122","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Versatile electromagnetic vortex beamforming for phased array using hybrid neural network-based modeling and optimization","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.114122","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"114122"}}